Introduction to statistics...ppt rahul
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INTRODUCTION TO
STATISTICS
R Dh@ker, Lecturer, PCNMS 1
INTRODUCTION
The word statistics conveys a variety
of meaning to people in different walks
of life.
2R Dh@ker, Lecturer, PCNMS
The word statistics comes from the
Italian words Statista
( Statement).
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CONT…INTRODUCTION
The German word Statistik
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Political state
The word Statistics today refers to
either quantitative information or a
method of delaling with quantitative
or qualitative information.
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DEFINITION “Statistics is defined as collection,
Presentation, analysis and interpretation of
numerical data”. Acc. Croxton & cowden
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statistics is the sciences and art of
dealing with figure and facts.
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Biostatistics Biostatistics is the branch of statistics
applied to biological or medical
sciences.
Biostatistics is the methods used in
dealing with statistics in the field of
health sciences such as biology,
medicine, nursing, public health etc.
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Biostatistics is the branch of statistics
applied to biology or medical sciences.
Biostatistics is also called “Biometry”
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In Greek, Bios Life
Metron
So, it is measurement of life
Measured
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USE & APPLICATION OF STATISTICS
It facilitates comparisons
It simplifies the message of figure
It helps in formulating and testing
hypothesis
It help in prediction
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SCALE OF MEASUREMENT
Measurement is the process of assigning numbers
or labels to objects, persons, states, or events in
accordance with specific rules to represent
quantities or qualities of attributes.
We do not measure specific objects, persons, etc.,
we measure attributes or features that define them.
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Nominal ScalesNominal Scales
Ordinal ScalesOrdinal Scales
Interval ScalesInterval Scales
Ratio ScalesRatio Scales
FOUR BASIC SCALES OF MEASUREMENT
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Types of
Measurement Scales R
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Nominal measurement
There must be distinct classes but these classes have no quantitative properties. Therefore, no comparison can be made in terms of one category being higher than the other.
For example - there are two classes for the variable gender - males and females. There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable.
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CONT…NOMINAL SCALE
Sometimes numbers are used to
designate category membership-
Example: Country of Origin
1 = United States 3 = Canada2 = Mexico 4 = Other
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There are distinct classes but these classes have a natural ordering or ranking. The differences can be ordered on the basis of magnitude.
For example - final position of horses in a thoroughbred race is an ordinal variable. The horses finish first, second, third, fourth, and so on. The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth. 13
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Ordinal Scales
CONT…ORDINAL SCALES
Does not assume that the intervals between numbers are equal
Example:
finishing place in a race (first place, second place)
1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours
1st place 2nd place 3rd place 4th place
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INTERVAL SCALES It is possible to compare differences in magnitude,
but importantly the zero point does not have a natural meaning. It captures the properties of nominal and ordinal scales - used by most psychological tests.
Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5
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We can see that the same difference exists between 10o C ( 50 F) and 20 degree C ( 68 F)
25 C ( 77F) and 35 C ( 95 F)
But we can not say that 20C is twice as hot as a temperature of 10C
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Example - Celsius temperature is an interval
variable. It is meaningful to say that 25 degrees
Celsius is 3 degrees hotter than 22 degrees Celsius,
and that 17 degrees Celsius is the same amount hotter
(3 degrees) than 14 degrees Celsius. Notice,
however, that 0 degrees Celsius does not have a
natural meaning. That is, 0 degrees Celsius does not
mean the absence of heat!
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RATIO SCALESIt is the highest level for measurement
This level has all the three attributes:
Magnitude
Equal interval
Absolute zero point
It represent continuous values
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Example:
Biophysical parameters
Weight
Height
Volume
Blood pressure
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30 Kg is thrice of 10 kg
20 cm is twice of 10 cm
8 hours is four time of 2 hours
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TYPES OF MEASUREMENT SCALES (CONT.)
Each of these scales have different properties
(i.e., difference, magnitude, equal intervals, or
a true zero point) and allows for different
interpretations.
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The scales are listed in hierarchical order.
Nominal scales have the fewest measurement
properties and ratio having the most properties
including the properties of all the scales beneath
it on the hierarchy.
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TYPES OF MEASUREMENT SCALES (CONT.)
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The goal is to be able to identify the type of
measurement scale, and to understand proper
use and interpretation of the scale.
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TYPES OF MEASUREMENT SCALES
(CONT.)
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Bob
Gene
Sam
PRIMARY SCALES OF MEASUREMENT
ScaleNominal Symbols
Assigned to Runners
Ordinal Rank Orderof Winners
Interval PerformanceRating on a
0 to 10 Scale
Ratio Time to Finish, in
Seconds
3rd place 2nd place 1st place
Finish
Finish
3 7 9
15.2 14.1 13.4
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Scale Basic
Characteristics
Common Examples
Marketing Examples
Nominal Numbers identify & classify objects
Social Security nos., numbering of football players
Brand nos., store types
Ordinal Nos. indicate the relative positions of objects but not the magnitude of differences between them
Quality rankings, rankings of teams in a tournament
Preference rankings, market position, social class
Interval Differences between objects can be compared, zero point is arbitrary
Temperature (Fahrenheit) Celsius)
Attitudes, opinions, index nos.
Ratio Zero point is fixed, ratios of scale values can be compared
Length, weight Age, sales, income, costs
Descriptive statistics
Descriptive statistics use to organize and
summarize the data to draw meaningful
interpretations.
Descriptive statistics deal with the
enumeration, organization and graphical
representation of data.
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CONT…DESCRIPTIVE STATISTICS
Descriptive statistics includes-
Measures to condense data
Measures of central tendency
Measures of dispersion
Measures of relationship ( Correlation
coefficient)
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Measures to condense data
Frequency and percentage distribution through
tabulation and graphic presentation.
Table
Graphs and diagrams
Percentages
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Table Type
Frequency distribution
table
Contingency table
Multiple Response table
Miscellaneous table R Dh@ker, Lecturer, PCNMS
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FREQUENCY DISTRIBUTION TABLE
The data may be qualitative or quantitative
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The following are the weight in kg 48 medical students. Construct the frequency distribution table
50, 61, 70 71 63 34 75 80 45
56 57 58 60 62 72 78 48 50 63
64 67 52 52 54 55 56 57 70 71
72 73 64 65 66 67 62 63 65 52
60 54 56 58 57 61 81 82 80
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RELATIVE FREQUENCY
Relative frequency = Class frequency---------------------------Total frequency
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FREQUENCY DENSITY OF A CLASS
Frequency density of a class=frequency of the class------------------------------- width of the class
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105 100 109 106 122 103 122 107
102 105 103 100 119 116 120 122
115 119 118 109 103 108 106 107
104 103 105 102 106 103 109 114
122 114 100 116 115 110 120 100
117 120 107 116 119 122 122 107
106 117
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138 164 150 132 144 125 149 157 146 158 140 109 136 148 152 144 168 126 138 186 163 109 154 165 146 183 105 108 135 153 140 135 161 145 135 142 150 156 145 128
GRAPHS AND DIAGRAMS
Type
Bar diagram
Pie chart
Histogram
Frequency
polygon
Line diagram R Dh@ker, Lecturer, PCNMS
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Cumulative
frequency curve
Scattered diagram
Pictograms
Map diagrams
CONT…GRAPHS AND DIAGRAMS
Presentation of quantitative, continuous or measured data is through graphs. The common graphs in use are:-
Histogram Frequency polygon Frequency curveLine chart or graphCumulative frequency diagram Scatter or dot diagram
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Presentation of qualitative , discrete or
counted data is through diagrams. The
common diagrams in use are:-
Bar diagram
Pie diagram
Pictogram diagram
Map diagram or spot map R Dh@ker, Lecturer, PCNMS
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CONT…Graphs and diagrams
Measures of central tendency
Arithmetic mean
Median
Mode
Geometric mean
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MEASUREMENT OF CENTRAL TENDENCY
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Sl. no Data levelCharacteristics Measurement of central
tendency
1 NominalMeasured on scale of
frequency of categories Mode (Mo)
2 OrdinalMeasured on no scale but
can be ranked Median (Md)
3 IntervalMeasured on a scale with no
true zero Mean (M)
4 RatioMeasured on a scale with
absolute zero Mean (M)
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